The origin of magnetization-caused increment in water oxidation

Magnetization promoted activity of magnetic catalysts towards the oxygen evolution reaction (OER) has attracted great attention, but remains a puzzle where the increment comes from. Magnetization of a ferromagnetic material only changes its magnetic domain structure. It does not directly change the spin orientation of unpaired electrons in the material. The confusion is that each magnetic domain is a small magnet and theoretically the spin-polarization promoted OER already occurs on these magnetic domains, and thus the enhancement should have been achieved without magnetization. Here, we demonstrate that the enhancement comes from the disappeared domain wall upon magnetization. Magnetization leads to the evolution of the magnetic domain structure, from a multi-domain one to a single domain one, in which the domain wall disappears. The surface occupied by the domain wall is reformatted into one by a single domain, on which the OER follows the spin-facilitated pathways and thus the overall increment on the electrode occurs. This study fills the missing gap for understanding the spin-polarized OER and it further explains the type of ferromagnetic catalysts which can give increment by magnetization.

I thank the authors for their efforts to answer the concerns raised in the previous review round. However, after careful consideration, I am still not convinced that the conclusions are fully supported by the data.
The oxygen evolution reaction happens at the surface of the catalyst, and hence any increase in the efficiency must be explained by surface properties. As I will show below, this is currently not the case. MFM is a technique which measures magnetic stray fields, which for the structures considered here are generated by a small out-of-plane tilt of the magnetization at the surface, originating in the bulk magnetization structure. The bulk magnetization consists of large out-of-plane domains, separated by sharp domain walls. This structure is slightly reflected in the magnetization at the surface, which has a small out-of-plane tilt of about 10%. This means that the MFM images are blind to about 90% of the magnetization texture at the surface. The authors compare the MFM images to the amount of out-ofplane magnetization extracted from micromagnetic simulations (and have clarified in their response that they calculate this also over the entire bulk of the simulations, instead of only at the surface). This means that both quantities are seemingly in agreement, but give little information on what is happening at the surface.
As I have already mentioned in my previous review report, the surface contains in-plane closure domains with a more complex domain wall structure than the one visible in the MFM pictures.To illustrate this point, I have attached four figures of the same structure, two with a color scheme similar to the one used by the authors which only shows the out-of-plane magnetization in red/blue and the inplane in white (which therefore hides all in-plane magnetization structures); and two with a color scheme which shows the out-of-plane components in white/black and the different in-plane magnetization directions in different colors. As is clearly visible, the surface is magnetized almost fully in-plane with a much less clear-cut division in domains and domain walls, but rather display a continuously changing magnetization direction.
Furthermore, I have repeated the authors' simulations and quantified the out-of-plane magnetization *only* at the surface layer, instead of in the bulk, and have found that this varies much less strongly (from about 10% for 200 nm thick films to about 9% for 800 nm thick films).
The authors do find an interesting correlation between the stray fields at the surface (reflecting the underlying domain structure in the bulk of the material) and the OER enhancement, but because at the surface there is a very different domain structure present than the one with which the authors correlate their findings, the current explanation based on the relative area occupied by domains and domain walls cannot be the complete picture.
Moreover, the correlation, as depicted in figure 4, is visually misleading, because both axes have an offset with respect to the origin, and when extrapolating the data towards thicker films, where the domain wall area would fall below 5%, a negative OER increase would even be expected, which clearly would contradict the presented explanation.
Finally, besides the observation that there might be a correlation (and please note that correlation does not imply causation) between the OER increase and the stray fields, there is no explanation of the microscopic process underlying this enhancement (which was the main claim of the paper). The conclusion that "This study has addressed the origin of the OER increment on ferromagnetic catalyst" is therefore unsubstantiated.
The only thing that comes close to an explanation, i.e. lines 189 and following: "... the unpaired electrons in domain wall are in a transition region in which the spin direction is affected by two neighbor domains with opposite magnetization direction and are highly disordered." is unconvincing. Reference 22 which was cited in this context also does not contain any statements on disorder in the spin directions. The OER is a reaction that takes place on atomic length scales, and therefore should be influenced by the local environment only. In contrast, the domain walls at the surface vary much more gradually over length scales of about 20 nm, and except for not being exactly aligned with their neighbors, the spins are not at all disordered.
A few technical comments: -The description of the anisotropy used in the simulations is not correct. There is a difference between a system with 2 uniaxial anisotropies, i.e. a biaxial anisotropy with 4 easy directions of the magnetization, and the system described by the authors consisting of a single uniaxial anisotropy which is slightly tilted such that the anisotropy vector has both an in-plane and out-of-plane component. The top of the method section makes clear that the latter implementation was used, but the description in the remainder of the manuscript is ambiguous.
- Figure 2 in the manuscript still shows Mz in the legend, despite the correction to "MFM phase shift" that was mentioned by the authors on page 31 of their response.
In short, I still find the conclusions insufficiently supported by the results, and find a major revision necessary before the manuscript can be considered for publication, either in this journal or elsewhere.
1 Reviewer #1 (Remarks to the Author): Thanks to the authors for the hard work and discussions on their manuscript. From my point of view and after reading all the responses to the reviewers, I think that the manuscript should be accepted at n. communications But, before acceptance, I'd like some clarification on the electrochemical setup (I apologise, I missed it in the previous review).
In the schematic setup, videos and photos, I noted that the authors used the reference electrode on the cathode side. So I would like to know why the authors used this configuration. Normally, in electro-catalysis the reference electrode (RE) must be close to the working electrode (WE) (in this case NiFe alloy) to know the voltage changes during the reaction (in this case OER). So, I'm surprised or maybe I don't understand the motivation to track the changes in the WE, just by placing the RE near the cathode side.
Response: Thanks for the comment. We designed the cell in such a way to ensure that the two heads of the electromagnet are very close to each other. This will help to get the desired field strength at a small power input to the electromagnet. Otherwise, a high-power input has to be applied and it will result in a heating effect from the electromagnet to the electrochemical cell in between.
Reviewer #2 (Remarks to the Author): In the revised manuscript, Ren et al. have addressed the points of discussion raised by the referees. I recommend publication after addressing the few remaining points below.
-In response figure R15, the authors infer Ni3+ states, i.e. NiOOH. Yet based on a Pourbaix diagram, one would expect this phase to be present only at high oxidizing potentials, e.g. during OER. But once the potential is removed, one would expect a Ni(OH)2, and therefore Ni2+ oxidation state. This should be further elaborated.
Response: Thanks for the reviewer's suggestion. We have fit the 2p2/3 orbitals of Ni and Fe as shown in the figure below ( Figure R1 in this response letter). The metallic Fe and Ni (labeled as Fe 0 and Ni 0 ) with narrow peaks can be found in the film samples. After the electrochemical tests, the peaks of Fe 0 become weakened and the XPS spectra of Ni 2p3/2 can be fitted with two characteristic peaks at 855.2 and 856.2 eV, which are associated with the formation of Ni(OH)2 and NiOOH, respectively (Surf. Interface Anal. 2009, 41, 324−332). The result indicates that the NiFeOxHy is formed on the surface. These data have been updated in SI (Line 174, page 15 in SI, marked in red) Figure R1 & Supplementary Fig.12. The Ni and Fe 2p for all NiFe films before and after the electrochemical tests.
-The authors now included changes in EIS-derived resistances. It would help if they could also demonstrate that magnetoresistance is not the cause of the enhancement by showing resistivity vs. magnetic field measurements.
Response: Thanks for the suggestion. Figure R2 shows the magnetoresistance (MR) of three samples under the magnetic field. The MR of the NiFe films is very small. We did not find any correlation between the MR change and the film thickness. Indeed, the measurement demonstrates that MR is not the cause of the enhancement. -In the revised version, there are grammatical mistakes in the added sentences.

Response:
We have checked writing in the revised manuscript and corrected mistakes (marked in red in the revised manuscript).
Reviewer #4 (Remarks to the Author): I thank the authors for their efforts to answer the concerns raised in the previous review round. However, after careful consideration, I am still not convinced that the conclusions are fully supported by the data.
The oxygen evolution reaction happens at the surface of the catalyst, and hence any increase in the efficiency must be explained by surface properties. As I will show below, this is currently not the case. MFM is a technique which measures magnetic stray fields, which for the structures considered here are generated by a small out-of-plane tilt of the magnetization at the surface, originating in the bulk magnetization structure. The bulk magnetization consists of large out-ofplane domains, separated by sharp domain walls. This structure is slightly reflected in the magnetization at the surface, which has a small out-of-plane tilt of about 10%. This means that the MFM images are blind to about 90% of the magnetization texture at the surface. The authors compare the MFM images to the amount of out-of-plane magnetization extracted from micromagnetic simulations (and have clarified in their response that they calculate this also over the entire bulk of the simulations, instead of only at the surface). This means that both quantities are seemingly in agreement, but give little information on what is happening at the surface.
As I have already mentioned in my previous review report, the surface contains in-plane closure domains with a more complex domain wall structure than the one visible in the MFM pictures. To illustrate this point, I have attached four figures of the same structure, two with a color scheme similar to the one used by the authors which only shows the out-of-plane magnetization in red/blue and the in-plane in white (which therefore hides all in-plane magnetization structures); 4 and two with a color scheme which shows the out-of-plane components in white/black and the different in-plane magnetization directions in different colors. As is clearly visible, the surface is magnetized almost fully in-plane with a much less clear-cut division in domains and domain walls, but rather display a continuously changing magnetization direction.
Furthermore, I have repeated the authors' simulations and quantified the out-of-plane magnetization *only* at the surface layer, instead of in the bulk, and have found that this varies much less strongly (from about 10% for 200 nm thick films to about 9% for 800 nm thick films).
The authors do find an interesting correlation between the stray fields at the surface (reflecting the underlying domain structure in the bulk of the material) and the OER enhancement, but because at the surface there is a very different domain structure present than the one with which the authors correlate their findings, the current explanation based on the relative area occupied by domains and domain walls cannot be the complete picture.

Response: Thanks for the further questions.
First, we agree that the oxygen evolution reaction happens at the surface of the catalyst. But, the well-accepted thicknesses of "surface" has a few nanometers to tens of nanometers by previously reported (Nature Chem 9, 457-465 (2017); Sci. Adv. 3, e1603206 (2017)). In this work, the minimum depth of the catalyst film surface involved in the reaction is about 11 nm as shown in Supplementary 14. In micromagnetic simulations, the depth of the surface is determined by the set cell size. We set the cell in this work based on the reviewer's suggestion in which the depth of this surface is about 4 nm. This thickness in micromagnetic simulations are much less than the thickness of the actual reaction surface region.
Second, we appreciate the simulated domain structure done by the reviewer and fully agree. The arrangement of magnetic moments on the surface is more complex than in the bulk, but these two are directly correlated, that is, the periodic arrangement of the magnetic domains and domain walls directly determines the magnetic configuration of the surface. The in-plane variation of the surface magnetic moment over a full stripe period can be determined as -π/2, 0, π/2, 0,π/2. The in-plane variation period of the surface magnetic moment remains constant as the domain width changes as depicted in Figure R3. The average angle of the magnetic moment within a period is related to the stripe period. The direction of the magnetic moment inside the bulk domain changes slowly, the direction of the magnetic moment at the domain wall changes faster. The magnetic moment at the surface follows the same rule. That is, the direction of the magnetic moment at the surface locate around |π/2| changes faster, and locate around 0 changes slowly. 5 Figure R3. Equilibrium magnetization distribution in bulk and surface obtained from micromagnetic simulation of NiFe-200 film.
Third, it should be emphasized that the OER enhancement is from the magnetization. The reviewer paid much attention on the status without magnetization but should not ignore the change after magnetization, which should be paid more attention on. This is a clear case of the amount of change in the magnetic state after the magnetization (application of the magnetic field). We further calculated the rate of change of the magnetic moment along the x-direction of the surface shown in Figure R4. The variation of magnetic moment is small in the domain region and large in the domain wall region. The rate of change of the magnetic moment at the surface corresponding to the domain wall shows a clear thickness dependence, i.e., the thicker the film and the wider the stripe, the smaller the rate of change of the magnetic moment. When the magnetic field is applied, all magnetic moment is pulled parallel. The thinner the sample, the greater the change in magnetic moment. It is exactly what have been observed. Figure R4. a. The difference between two adjacent magnetic moments at different positions in the X-direction on the surfaces of samples with different thickness; b. The average rate of change of magnetic moment over a full stripe period. 6 Overall, the thicker the film the higher the polarization(the smaller domain walls occupied), the smaller the OER enhancement under magnetic field.
Moreover, the correlation, as depicted in figure 4, is visually misleading, because both axes have an offset with respect to the origin, and when extrapolating the data towards thicker films, where the domain wall area would fall below 5%, a negative OER increase would even be expected, which clearly would contradict the presented explanation.
Response: Typically, the magnetic moments of NiFe sample mainly lie in the plane of the thin film due to the relatively strong demagnetization energy of film. However, an out-of-plane magnetization component of NiFe film arises above a critical film thickness, and an array of oscillating 'up and down' magnetic stripe domains forms due to the predominant factor in the perpendicular anisotropy. We have selected samples with significant variation in stripe domain width from 200-800 nm of thickness. Extending this correlation to thickness beyond the designated range will be problematic in the model films, because in thinner or thicker samples there may be formation of domains in non-stripe structure.
Finally, besides the observation that there might be a correlation (and please note that correlation does not imply causation) between the OER increase and the stray fields, there is no explanation of the microscopic process underlying this enhancement (which was the main claim of the paper). The conclusion that "This study has addressed the origin of the OER increment on ferromagnetic catalyst" is therefore unsubstantiated.
The only thing that comes close to an explanation, i.e. lines 189 and following: "... the unpaired electrons in domain wall are in a transition region in which the spin direction is affected by two neighbor domains with opposite magnetization direction and are highly disordered." is unconvincing. Reference 22 which was cited in this context also does not contain any statements on disorder in the spin directions. The OER is a reaction that takes place on atomic length scales, and therefore should be influenced by the local environment only. In contrast, the domain walls at the surface vary much more gradually over length scales of about 20 nm, and except for not being exactly aligned with their neighbors, the spins are not at all disordered.

Response:
We have to strongly disagree with the reviewer. The microscopic process of spinpolarized OER has been reported in previous works (Phys. Chem. Chem. Phys., 2017, 19, 20451;Journal of Catalysis 2018, 361, 331-338;Phys. Chem. Chem. Phys., 2019, 21, 2977-2983J. Phys. Chem. C 2019, 123, 9967-9972;Nat Communications, 2021, 12, 2608ACS Catal. 2021, 11, 14249−14261;Current Opinion in Electrochemistry 2021, 30, 100804, etc.). Based on those understandings, one cannot explain why magnetization can enhance the activity. Because a ferromagnetic catalyst consists of many small domains, each of which can be treated as a small magnet. On these small magnets, the spin-polarized OER already exists as indicated in those studies. Respectively saying, if the reviewer really understands the background of this direction, the reviewer should have the same question where the OER enhancement comes from under the magnetization. This work demonstrates the origin of the enhancement. Thus, we strongly disagree with the reviewer about his/her opinion.
In addition, we refer to the Ref. 22 schematic diagram (the Figure 1 in reference) to illustrate the characteristics of domain and domain wall. Considering the suggestion of the reviewer, we added the reference(C. Kittel, Rev. Mod. Phys. 21, 541 (1949).) in the revised manuscript marked in red.
A few technical comments: -The description of the anisotropy used in the simulations is not correct. There is a difference between a system with 2 uniaxial anisotropies, i.e. a biaxial anisotropy with 4 easy directions of the magnetization, and the system described by the authors consisting of a single uniaxial anisotropy which is slightly tilted such that the anisotropy vector has both an in-plane and out-ofplane component. The top of the method section makes clear that the latter implementation was used, but the description in the remainder of the manuscript is ambiguous.
Response: Thanks. We have corrected the description "in-plane and perpendicular magnetic anisotropy were applied" to "perpendicular magnetic anisotropy with slight tilt were applied" at the method section (marked in red in revised manuscript).
- Figure 2 in the manuscript still shows Mz in the legend, despite the correction to "MFM phase shift" that was mentioned by the authors on page 31 of their response.

Response:
Thanks for pointing this out. We have updated the Figure 2 in the revised manuscript. In short, I still find the conclusions insufficiently supported by the results, and find a major revision necessary before the manuscript can be considered for publication, either in this journal or elsewhere. In my opinion, publication in this journal requires a deeper understanding that goes beyond the description of an observed correlation.